David Bailey

Parquet Deformations of David Bailey
 


Below I show some examples of my own parquet deformations that I consider to be (or are largely) ‘aesthetic’, from my archive. These number about 100 works, but possibly extending to about 200. These are mostly square-based, with on occasion on equilateral triangles and hexagons (not shown here yet). These are of a variety of dates (I return to the study ad hoc), from 1987 onwards, but are mostly of 1993, or at least the latter is of a concerted period of study of that year. These were originally hand-drawn, and of which I have latterly computer redrawn in Rhino, of February-April 2021. Note that this page is very much a work in progress; the final presentation and format is to be decided. Since its instigation in February 2021, the page has developed and changed considerably. With time, less change, upon a decided arrangement that will evolve, will occur. As I am in the process of redrawing the existing hand-drawn examples in Rhino, I will add these here at short intervals upon completion.

The present format is of a parquet deformation followed by some brief text. This concerns a unique identifier, of ‘country and towns’ (this ‘oddness’ is explained below), the original date of drawing (which enables me to find the parquet deformation easily in my chronologically arranged files! Further, not all of these were drawn out as a finished work at the time, which complicates matters somewhat. Be that as it may, the date given is at least an indication of when that work was at least initiated or in some recognisable form as to the page here) I then add the date of when it was redrawn in Rhino. Finally, I describe the transition, e.g. from squares to rectangles, with a general commentary, with later more detailed and expansive text to follow in due course.

Identifying/referencing each work is (perhaps surprisingly) problematic. I have so many that it is impractical to name/title these in the same imaginative way that Huff did with his students' work. A simple (and obvious) description of the beginning and end tiles, e.g. squares to right-angled triangles soon runs into repeats, with confusion as to which deformation thus arises. What is needed is a unique identifier. An obvious possibility is simply ‘parquet deformation 1, 2, 3..’. etc. However, in practice, there are problems here. As alluded to above, there is no strict order of sequence. Some are incomplete, in sketch form. Some are of a photocopied sheet of a grid filled in. Others are a finished drawing from yesteryear from a sketch. Some are of a second generation i.e. grid to parquet deformation, and then an addition. Confusion personified! To this end, I retain an old idiosyncratic system I used from my earliest days, likely much to the chagrin of any mathematician reading this! As each instance overwhelmingly follows a typical process of an ‘open grid’ and subsequent ‘filling-in’ (to greater (second generation)  or lesser (first generation) degrees, I use a two-part system, where I title the open grid after a country, with the ‘filling-in’ of towns/cities thereof. For example Canada (grid)  - Ottawa (filling-in); Canada - Banff etc. Although not strictly mathematical, it makes referring to any specific parquet deformation and its underlying grid much easier than trying to remember a strictly mathematical procedure e.g. instance 64 (grid) and what 64a, 64b, 64c (variations) represents, or, even more involved, with second generation instances, e.g. 64a(i)!. Of course, I could have used any other ‘two-part’ system; there is nothing unique about the ‘country and town’ system.


Below I show some examples of my own that I consider ‘aesthetic’ (dating from 1987), numbering about 100, but possibly extending to about 200 works. These are mostly square-based, with on occasion based on equilateral triangles and hexagons. Note that this is very much a work in progress; I am in the process of redrawing existing hand-drawn examples in Rhino, of which I will add here at short intervals, with later accompanying text.

Inventory. Largely for my own record keeping! I have so many parquet deformations, with many variations, that keeping track of what I have added to the page is inconvenient. Further, everything is in a state of flux, with drawing in Rhino learnt as I go along. The listing numbering is to be considered as first attempt at a degree of order. This at least enables me to see at-a-glance what I have added without time-consuming and (ever increasing) scrolling.

1. France (Old) To be renamed 2. France - Paris. To be renamed. 3. France - Lyon 4. Argentina - Buenos Aires
5. Anon
6. Mexico - Acapulco
7. Canada - Ottawa
8. Canada - Banff
9. Canada - Anon
10. USA - New York
11. USA  - Minneapolis
12. USA 
 - Minneapolis 2
13. USA - New York subdivided
14. USA - Baltimore
15. USA - Baltimore
16. USA - Baltimore (coloured lines)
17. French Guiana - Cayenne
18. French Guiana - Cayenne reflected
19. French Guiana - Cayenne superimposed with vertices moved to midpoint of cell.
20. French Guiana - Matoury
21. 
Libya - Tripoli
22. Libya - Misurata
23. Libya - Sabratha
24. Ecuador - Ambato
25. Ecuador - Cuenca
26. Belgium - Brussels
27. Kenya - Nairobi
28. Brazil - Rio De Janeiro
29. Brazil - Belo Horizonte
30. Brazil - Curitiba
31. Brazil - Sao Paulo 
32. Venezuela - Caracas
33. Venezuela - Pampatar
34. Venezuela - Guarenas
35. Venezuela - Barquisimeto
36. Venezuela - Mataray
37. Venezuela - Macaray
38. Venezuela - Cumana
39. England - York
40. England - London
41. England - Lincoln
42. Guyana - Georgetown - New Amsterdam
43. Guyana - Georgetown - Linden
44. Portugal - Funchal
45. Portugal - Porto
46. Portugal - Faro
47. Portugal - Coimbra
48. Portugal - Faro
49. Suriname - Paramaribo
50. Suriname - Lelydorp
51. Tunisia - Bizerte
52. Tunisia - Hammamet
53. Tunisia - Kairoaun
54. Tunisia - Sousse
55. Tunisia - Tunis
56. Cuba - Camaguey
57. Cuba - Havana
58. Cuba - Santa Clara
59. Cuba - Veradero
60. Italy - Rome
61. India - Delhi
62. India - Calcutta
63. Romania - Bucharest
64. Romania - Cluj-Napoka (Bucharest Double Basketweave subdivided)
65. Romania - Timisoura (same as England, London!)
66. Switzerland - Zurich
67. Switzerland - Basel
68. Switzerland - Geneva
69. Switzerland - Zermatt
70. Netherlands - Amsterdam
71. Netherlands - Rotterdam

The Parquet Deformations

1. France - Paris. Originally 15 May 1989. Redrawn in Rhino 2021*
Transitions from square to right-angled triangles (with rectangles mid-stream). This is in particular elegant, and a favourite. Described as minimalist.

2. France - Paris. Superimposition. New 4 March 2021

3. France - Lyon. Originally 2 July 1993. Redrawn in Rhino 5 March 2021  
Transitions from right-angled triangles to right-angled triangles (with squares mid-stream). A curious feature is the lines at 45° throughout. Another interpretation is Paris rotated 180° and superimposed. Elegant.

4. Argentina - Buenos Aires. Originally 1989, and again 1993. 
Redrawn in Rhino 2021.* (No. 5 on main page)
Transitions from squares to rectangles, at 45°This is in particular elegant, and a favourite. Described as minimalist.



5. Originally 28 June 1993. Redrawn in Rhino 2021.
Transitions from squares at 45° to right-angled triangles, set within a subdivided square

6. Mexico - Acapulco. Originally 28 June 1993

7. Canada - Ottawa. Originally 28 June 1993. Redrawn in Rhino 2021
Transitions from squares of two sizes to Greek crosses. 
 

8. Canada - Banff. Originally 28 June 1993. Redrawn in Rhino 2021

9. Canada. 2 March 2021.


10. USA - New York. Originally 28 June1993. Redrawn in Rhino 2021


11. USA - Minneapolis. Originally 28 June 1993. Redrawn in Rhino 2021

12. USA - Minneapolis. Overlay. New 9 March 2021


13. USA - New York subdivided. 8 March 2021

14. USA - Baltimore (New). 8 March 2021

15. USA - Baltimore Subdivided (New). 9 March 2021

16. USA - Baltimore Subdivided (New). 11 March 2021

17. French Guiana - Cayenne. Originally 28 June 1993. Redrawn 10 March 2021*
Transitions from squares to four right-angled triangles within a square.

18. French Guiana - Cayenne reflected and directly superimposed. New 10 March 2021

19. French Guiana - Cayenne superimposed with vertices moved to midpoint of cell. New 10 March 2021

20. French Guiana - Matoury. Originally 28 June 1993. Redrawn in Rhino 10 March 2021*
Transitions from squares to squares at 45°.

21. Libya - Tripoli. 
Originally 2 July 1993. Redrawn in Rhino 11 March 2021*
Transitions from squares to two right-angled triangles set within a square. However, the transition overall lacks elegance, with intermediate tiles of no particular aesthetic. It's only merit is the beginning and end transition itself, as a specific design solution. However, as can be seen on this page, I am not short of such specifics!

22. Libya - Misurata. Originally 2 July 1993. Redrawn in Rhino 11 March 2021*
Transitions from squares to squares, with symmetrical intermediary tiles.

23. Libya - Sabratha. 11 March 2021 New*
Transitions from parallelograms to squares. However, the transition overall lacks elegance, with intermediate tiles of no particular aesthetic, of 'elongated' tiles without symmetry. It's only merit is the beginning and end transition itself, as a specific design solution

24. Ecuador - Ambato. Originally  28 June 1993. Redrawn in Rhino 12 March 2021
Begins and ends with the same square tiles, at 45°, as a consequence of its natural cycle (as against an inferior unravelling at the middle, back to square), which gives a pleasing cohesion. 

25. Ecuador - Cuenca. New. Drawn in Rhino 12 March 2021
An unusual instance, of overlapping lines at the right-hand side

26. Belgium - Brussels. Originally 1993. Redrawn in Rhino 15 March 2021. (No. 6 on main page)
Transitions from rectangles at 45° to two right-angled triangles within a squareVery nice, minimalistic, a favourite.

27. Kenya - Nairobi. Originally 1993. Redrawn in Rhino 15 March 2021.*
Transitions from squares to two right-angled triangles within a square. Very nice, minimalistic, a favourite.

28. Brazil - Rio De Janeiro. Originally 21 June 1993. Redrawn in Rhino 16 March 2021.*
Transitions from squares to squares at 45°

29. Brazil - Belo Horizonte. Originally 23 June 1993. 
Redrawn in Rhino 16 March 2021. Composed by suitably subdividing Brazil - Rio De Janeiro
Transitions from double basketweave to squares at 45°. Very nice, with the pleasing feature of the tiling overlapping at 90°

30. Brazil - Curitiba. Originally 1993? Redrawn in Rhino 16 March 2021. Composed by suitably subdividing Brazil - Rio De Janeiro
Transitions from a double basketweave tiling to four right-angled triangles set within a square

31. Brazil - Sao Paulo. Originally 23 June 1993. Redrawn in Rhino 16 March 2021. Composed by suitably subdividing Brazil - Rio De Janeiro
Transitions from a double basketweave tiling to squares at 45°.

32. Venezuela - Caracas. Originally 22 June 1993. 
Redrawn in Rhino 25 March 2021.
Transitions from squares to squares and four right-angled triangles with a square at 45°.

33. Venezuela - Pampatar (Caracas Subdivided). New. Drawn in Rhino 19 April 2021
Transitions from double basketweave to two sizes of right-angled triangles in an 'involved' arrangement that is hard to describe!

34. Venezuela - Guarenas 
(Caracas Subdivided). New. Drawn in Rhino 19 April 2021
Transitions from double basketweave to two sizes of right-angled triangles in an 'involved' arrangement that is hard to describe!

35. Venezuela - Barquisimeto. Originally 1989? Redrawn in Rhino 25 March 2021. Composed by suitably subdividing Venezuela - Caracas
Transitions from a double basketweave tiling to large and small right angled triangles within two different sizes of squares

36. Venezuela - Mataray. New. 25 March 2021. Composed by suitably subdividing Venezuela - Caracas
Transitions from a double basketweave tiling to large and small right angled triangles within two different sizes of squares

37. Venezuela - Maracay.  Originally 22 June 1993. Redrawn in Rhino 25 March 2021.
Transitions from a double basketweave tiling to an overlapping series of lines that defies description!

38. Venezuela - Cumana. Originally 22 June 1993. Redrawn in Rhino 25 March 2021.

39. England - York. 
Originally 23 June 1993. Redrawn in Rhino 26 March 2021.

40. England - London. Originally 23 June 1993. Redrawn in Rhino 26 March 2021. (No. 10 on main page)

41. England - Lincoln. New. Drawn in Rhino 26 March 2021. Composed by suitably subdividing England - London.


42. Guyana - Georgetown - New Amsterdam (Georgetown subdivided)

43. Guyana - Georgetown - Linden (Georgetown Subdivided)


44. Portugal - Funchal. Originally? Redrawn in Rhino 30 March 2021 (No. 12 on main page)

45. Portugal - Porto. Originally 2 July 1993. Redrawn in Rhino 30 March 2021 (Funchal Subdivided) (No. 9 on main page)
Aesthetic. This shows the minima to maxima of the Cairo tiling.

46. Portugal - Faro. Originally 2 July 1993. Redrawn in Rhino 30 March 2021 (Funchal Subdivided)

47. Portugal - Lisbon. Originally? Redrawn in Rhino 30 March 2021 (Funchal Subdivided) (No. 7 on main page)
Aesthetic. Simple, but elegant.

48. Portugal - Coimbra. Originally 2 July 1993. Redrawn in Rhino 30 March 2021 (Funchal Subdivided)

49. Suriname - Paramaribo. Originally 28 June 1993. Redrawn in Rhino 31 March 2021*

50. Suriname - Lelydorp. Originally 28 June 1993. Redrawn in Rhino 31 March 2021
Transitions from parallelogram to parallelogram (of two right angled triangles), rotated 90°). 

51. Tunisia - Bizerte. New. Drawn in Rhino 2 April 2021
Transitions from parallelograms to rectangles at 45°.

52. Tunisia - Hammamet. New. Drawn in Rhino 2 April 2021
Transitions from reflected parallelograms to rectangles at 45°.


53. Tunisia - Kairoaun. New. Drawn in Rhino 2 April 2021
Transitions from squares to chevrons.


54. Tunisia - Sousse. New. Drawn in Rhino 2 April 2021*
Transitions from squares to rectangles at 45°.


55. Tunisia - Tunis. New. Drawn in Rhino 2 April 2021*
Transitions from squares to rectangles at 45°.

56. Cuba - Camaguey. Originally 28 June 1993. Redrawn in Rhino 17-18 April 2021
Transitions from pinwheels to four right angled triangles.

57. Cuba - Havana. Originally 28 June 1993. Redrawn in Rhino 17-18 April 2021

58. Cuba - Santa Clara. Originally 28 June 1993. Redrawn in Rhino 17-18 April 2021

59. Cuba - Veradero. New. Drawn in Rhino 17-18 April 2021


60. Italy - Rome. Drawn in Rhino 17-18 April 2021* (No. 4 on main page)

61. India - Delhi. Drawn in Rhino 12 April 2021

62. India - Delhi. Drawn in Rhino 12 April 2021


63. Romania - Bucharest. Drawn in Rhino 13 April 2021 (No. 8 on main page)

64. Romania - Cluj-Napoka (Bucharest Double Basketweave subdivided) Drawn in Rhino 13 April 2021 (No. 11 on main page)

65. Romania - Timisoara (same as England, London!). Drawn in Rhino 13 April 2021 (No. 10 on main page)

66. Switzerland - Zurich. 
Drawn in Rhino 5 April 2021

67. Switzerland - Basel. Drawn in Rhino 5 April 2021

68. Switzerland - Geneva. Drawn in Rhino 5 April 2021

69. Switzerland - Zermatt. Drawn in Rhino 5 April 2021

70. Netherlands - Amsterdam. Drawn in Rhino 9 May 2021. (No. 1 on main page)

71. Netherlands - Rotterdam. Drawn in Rhino 9 May 2021

72. Sudan - Atbara. New. Drawn in Rhino 12-13 May 2021
Transitions from squares  to chevrons. Also see No. 53. Tunisia - Kairoaun for another transition

73. Sudan - Kadugli. New. Drawn in Rhino 12-13 May 2021

74. Sudan - Kosti. New. Drawn in Rhino 12-13 May 2021
Transitions from squares and parallelograms to rectangles at 45 in a herringbone arrangement. 


ASSEMBLIES

Strips shown horizontally (750px)

1. Porto-Lisbon. New. Drawn in Rhino 6 April 2021

2. Porto-Belo Horizonte. New. Drawn in Rhino 7 April 2021

3. Argentina-Buenos Aires to Italy-Rome. Drawn in Rhino 10 May 2021 (750px)

Strip 3 shown vertically (1500px)





Specific Transitions
The above collection can be used to select as according to specific transitions, such as square to right-angled triangles, and see all the examples in any one transition, with the aim in mind of selecting a best, generally based on symmetry. Each specific transition has a brief commentary as to its merits (or otherwise!).

Each instance is titled in a dual manner, e.g. ‘Square to two right-angled triangles within a square/Two right-angled triangles within a square to square’. Simply stated, the reverse is possible by simply rotating the parquet deformation 180°, and so rather than in effect duplicating existing examples resulting in a very long listing, I thus show this dual ordering.

Inventory

1. Square to two right-angled triangles within a square/Two right-angled triangles within a square to square (4)

2. Square to Rectangle at 45°/Rectangles at 45° to Squares (4)

3. Square to Square (Self Dual) (1)

4. Square to four right-angled triangles within a square/Four right-angled triangles within a square to a square

5. Square to Parallelogram/Parallelogram to Square

6. Square to Small Square at 45°/Small Square at 45° to Square (2)

7. Rectangles at 45° to two right-angled triangles within a square/Two right-angled triangles within a square to rectangles at 45° (1)



1. Square to two right-angled triangles within a square/Two right-angled triangles within a square to square (4)

France - Paris

Libya - Tripoli

Kenya - Nairobi

Suriname - Paramaribo


2. Squares to Rectangles at 45°/Rectangles at 45° to Squares (4)

Argentina - Buenos Aires

Austria - Vienna


Tunisia - Sousse

Tunisia - Tunis

Italy - Rome

3. Square to Square (1)

Libya - Misurata

4. Square to four right-angled triangles within a square/Four right-angled triangles within a square to a square (2)

French Guiana - Cayenne

French Guiana - Cayenne Reflected horizontally

5. Square to Parallelogram/Parallelogram to Square




6. Squares to Small Squares at 45° (2)

French Guiana -
Matoury

Brazil - Rio De Janeiro


Large square at 45° to Four Right-Angled triangles/Four Right-Angled triangles to large square at 45° (1)

Mexico -


Rectangles at 45° to two right-angled triangles within a square/Two right-angled triangles within a square to rectangles at 45° (1)

Belgium - Brussels


Page created 18 February 2021. Last Updated 6 May 2021

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